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ClearAll@f; f[x_] := 2 Sin[x] - x - Log[x + 1] Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}]; orders = Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // ToString, {n, 0, nMax, 1}]; labels = MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, functions}];]; Plot[functions, {x, 0, 3}, PlotLabels -> labels, ImageSize -> 700, AspectRatio -> 1, PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1, PopupMenu}]

The above code ran with errors. How to modify it? I want to modify the code to make it universal. You can input any function and draw the corresponding function image and derivative image.

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2 Answers 2

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A TogglerBar is more flexible for the display of multiple functions. With it, you can select any combinations of functions.

ClearAll@f; f[x_] := 2 Sin[x] - x - Log[x + 1] colors = ColorData[97] /@ Range[11]; Manipulate[ funcs = Sort@funcs; functions = If[# == 0, HoldForm@f[x], HoldForm@D[f[x], {x, #}]] & /@ funcs; Plot[ Evaluate[ Tooltip[ ReleaseHold@#, StringForm["``=``", Hold@#, Simplify@ReleaseHold@#]] & /@ functions], {x, 0, 3}, PlotStyle -> (colors[[funcs + 1]]), Frame -> True, ImageSize -> Medium, AspectRatio -> 1, PlotLabel -> StringForm["`` = ``", HoldForm@f[x], f[x]], PlotLegends -> functions], {{funcs, {0, 1, 2}, "Functions"}, Prepend[Array[# -> HoldForm[Derivative[#][f][x]] &, 10], 0 -> HoldForm[f[x]]], ControlType -> TogglerBar}, SynchronousUpdating -> False, TrackedSymbols :> {funcs}]

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ClearAll["`*"]; f[x_] := (x - 1) E^x - x^2 xr = -10 <= x <= 10 gmax = Maximize[{f[x], xr}, x] gmin = Minimize[{f[x], xr}, x] lmax = Solve[{D[f[x], x] == 0, D[f[x], {x, 2}] < 0, xr}, x] lmin = Solve[{D[f[x], x] == 0, D[f[x], {x, 2}] > 0, xr}, x] Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}]; orders = Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // ToString, {n, 0, nMax, 1}]; labels = MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, functions}];]; Plot[{functions}, {x, -2, 2}, Epilog -> {{Darker@Green, AbsolutePointSize[20], Point[{x, f[x]} /. gmax[[2]]], AbsolutePointSize[16], White, Point[{x, f[x]} /. gmax[[2]]]}, {Darker@Red, AbsolutePointSize[20], Point[{x, f[x]} /. gmin[[2]]], AbsolutePointSize[16], White, Point[{x, f[x]} /. gmin[[2]]]}, AbsolutePointSize[8], Green, Point[{x, f[x]} /. lmin], Red, Point[{x, f[x]} /. lmax]}, PlotLabels -> labels, ImageSize -> 700, AspectRatio -> 1, PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1, PopupMenu}]
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